Efficient sampling of high-dimensional free energy landscapes using adaptive reinforced dynamics

Enhanced sampling methods such as metadynamics and umbrella sampling have become essential tools for exploring the configuration space of molecules and materials. At the same time, they have long faced a number of issues such as the inefficiency when dealing with a large number of collective variables (CVs) or systems with high free energy barriers. Here we show that, with clustering and adaptive tuning techniques, the reinforced dynamics (RiD) scheme can be used to efficiently explore the configuration space and free energy landscapes with a large number of CVs or systems with high free energy barriers. We illustrate this by studying various representative and challenging examples. First we demonstrate the efficiency of adaptive RiD compared with other methods and construct the nine-dimensional (9D) free energy landscape of a peptoid trimer, which has energy barriers of more than 8 kcal mol⁻¹. We then study the folding of the protein chignolin using 18 CVs. In this case, both the folding and unfolding rates are observed to be 4.30 μs⁻¹. Finally, we propose a protein structure refinement protocol based on RiD. This protocol allows us to efficiently employ more than 100 CVs for exploring the landscape of protein structures and it gives rise to an overall improvement of 14.6 units over the initial global distance test–high accuracy (GDT-HA) score.